Despite protests from residents who said it would make it more difficult to carry on petition drives, the Orlando City Council voted 4 to 2 Monday in favor of new rules for referendum initiatives in the city.

''You're virtually killing any future petition drives,'' said civic activist Roger Gaines, one of four people who spoke against the new law Monday. Others argued that it would violate residents' First Amendment rights to petition their governments.

The idea for the new law came up two years ago when Supervisor of Elections Betty Carter proposed that cities adopt uniform rules for petition drives that would make it easier to verify signatures. Her proposal calls for a separate printed page for each signature, so that the forms can be more easily alphabetized and verified.

But the law the city council adopted Monday also includes requirements that signatures be verified by the ''circulator'' of the petition.

Council members Mary Johnson and Mable Butler voted against the proposal. Butler said she couldn't support any measure that would be ''handicapping the citizenry.''

Gaines, who plans to seek election to the city council in 1986, said the new rules would add financial burdens to groups initiating petition drives.

If that rule was in effect when the nation was founded, Thomas Jefferson would have had to ''write out 56 different copies'' of the Declaration of Independence, he said.

As now written, the new law could stymie groups that use mail-in petitions by printing the proposal in mass-circulated newspapers or newsletters. Although the law expressly allows such mail-ins, the added requirement that signatures be verified by petition ''circulators'' could impair that effort.

''Maybe that is a problem,'' Mayor Bill Frederick said after the vote. He said he would ask city attorneys to research whether a ''circulator'' could be defined as the person who clips a petition and mails it in. If not, ''then we need to change it or correct it,'' he said.

Gaines said he is particularly concerned with the mail-in provision because he plans to use it for a new parks referendum he formally announced Monday. The Save Our Parks group, which is co-chaired by Central Florida Young Republicans President Doug Guetzloe, is seeking a change in the city charter to prohibit the city from selling any city parks or recreation areas without voter approval.

The group plans to circulate some of its petitions by printing them in the Orange County Sun, a weekly newspaper that Guetzloe publishes.

Council member Mary Johnson, who supports the parks proposal, tried to avoid that petition drive Monday by seeing if the council would agree to place it on the ballot.

Her proposal failed 4 to 2. Butler joined Johnson in voting for it.

Council member Glenda Hood, who opposed the measure, said her colleagues support parks but feel the referendum is unnecessary.

''There's only been one instance of a sale,'' she said. Last fall the city council agreed to sell Beardall Park to make way for the 35-story Sun Bank Center project.

The new law takes effect when it is received by the Secretary of State's office, which is expected to be about a week. Opponents said that if the law affects their petition drives they would decide then what to do about it.